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We present the linear stability analysis of horizontal Poiseuille flow in a fluid overlying a porous medium with anisotropic and inhomogeneous permeability. The generalized Darcy model is used to describe the flow in the porous medium with the Beavers-Joseph condition at the interface of the two layers and the eigenvalue problem is solved numerically. The effect of major system parameters on the stability characteristics is addressed in detail. It is shown that the anisotropic and inhomogeneous modulation of the permeability of the underlying porous layer provides an effective means for passive control of the flow stability.

Acoustic levitation has been the cornerstone of many interesting studies across multiple application domains ranging from biomedical engineering to spray drying. In the sphere of colloidal or nanofluid droplets, acoustic levitation allows researchers to probe deep into the physical mechanisms concerning stability, heat and mass transfer processes, and subsequent particle self-assembly. It also offers a plethora of opportunities to custom engineer the transport mechanisms, thereby enabling unique morphological features of the dried precipitate. The high degree of spatial control in a levitator and ease of experimental diagnostics ensure one to study any such transport process in great detail. In this review, we have systematically elucidated three important paradigms in acoustic levitation of nanofluid droplets. First, we have provided a detailed understanding of the fluid mechanics of the process by delving into the pressure and velocity fields the droplet encounters. We have provided descriptions about the key nondimensional number responsible for successful levitation of the droplet. Second, we have studied the transport processes in nanofluid droplets and investigated the important transport mechanisms that are affected by flow and the acoustic field of the levitator. In particular, we look into the heat and mass transfer limitation for particle laden droplets. Third, we have analyzed the particle self-assembly and formation of nanoporous viscoelastic shell. Subsequently, we provided detailed insights into the morphological transitions of the shell through buckling and cavity ingression. We also showcase how the morphology of the shell can be controlled using differential heating and doping. Finally, we conclude by showcasing some unique application context-like photonic crystal behavior that can emerge from unique particle assembly in acoustic levitation.

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